Pairwise comparison data are very common in daily life, especially in cases where the goal is to rank several objects. Rather than directly ranking all objects simultaneously, it is usually much easier and more efficient to first obtain results of pairwise comparisons and then use them to derive a global ranking across all individuals in
a principled manner. Since the required global rankings are not directly observable, developing a statistical framework for the estimating rankings is a challenging unsupervised learning problem.
One such statistical model for deriving global rankings using pairwise comparisons was presented in the classic paper [1]}, and thereafter commonly referred to as the Bradley-Terry model in the literature. A similar model was also studied by Zermelo [2]}. The Bradley-Terry model is one of the most popular models to analyze paired comparison data due to its interpretability and computational efficiency in parameter estimation. The Bradley-Terry model along with its variants has been studied and applied in various ranking applications across many domains. This includes the ranking of sports teams [3]}, [4]}, [5]}, scientific journals [6]}, [7]}, and the quality of several brands [8]}, [9]}, to name a few.
